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# Analyzing Statistical Studies

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## Statistical Study

A statistical study is an analysis of data gathered from a specific group, or population, to answer a question concerning the group. This is done by gathering various types of data:

• responses from interviews
• observations
• measurements
• counts

Statistical studies follow a standard general process.

When the population is large, it is often impractical to collect data from all test subjects. Thus, data can be obtained from a subgroup, or sample, of the population. If the sample maintains the demographics of the population, it is representative of the population.

## Sampling

Sampling is the process of selecting a sample from a population of objects or individuals. The sample can be then examined to make conclusions about the entire population.

Different sampling methods can be defined, for instance convenience sampling, self-selected sampling, systematic sampling, random sampling, stratified sampling, and cluster sampling. The following applet visualizes some of these methods.
Since it may be impractical, too expensive, or even impossible to examine every member of a population, sampling is often used in real-world scenarios. Consider the following examples.
• Baseball cards are divided by teams. Then five cards from each team are randomly selected to estimate the players' average RBIs.
• Every tenth person entering a music club is asked to name their favorite music genre.
• A website article on the tax increase invites readers to express their opinions on the government's decisions.
• A new drug is tested by a pharmaceutical company. Volunteers are divided randomly into two groups, one of which will receive the new drug, the second of which will receive a placebo.
The chosen sampling method influences the quality of results of a statistical study. To make accurate and useful conclusions about a population, it is important to select an unbiased sample, which is representative of the population that is examined.

## Determine if the sample is biased

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Two different samples are described below. Determine if it's a random sample or if it's biased.

1. The CEO of a company wants to know what the employees think of their working hours. She asks the employees to fill out a form.
2. Every third player in a women's football team is interviewed about the quality of their training equipment.
Show Solution expand_more

If a sample represents the population as a whole, the sample is said to be representative. If not, there is an error in the sampling called bias. Therefore, we should determine if each sample represents the population or not.

1. Since the employees are asked to fill out the form, they can choose to do so. Thus, it's possible that most people with a strong opinion about their working hours will participate. We can not be certain that the participants represent the whole population. Therefore, the sample is biased.
2. Since every third player is interviewed there is no specific group in the population that is chosen. Therefore, it's a random sample and its representative of the whole population.

## Hypothesis - Statistics

In analyzing a population, suspicions and expectations lead to making some assumptions or claims about population parameters. A claim about a parameter of a population is called a statistical hypothesis. These are some examples of statistical hypothesis.

• Smokers have a shorter life expectancy than non-smokers.
• The clients of a personal trainer lose an average of 24 pounds in the first 3 months of training.
• The medication Migraine Away is more effective against migraines than any other treatment.
• The mean human body temperature is
• The average height in the United States is 5 feet 4 inches for women and 5 feet 9 inches for men.
A statistical study can test a hypothesis to determine whether it is true or false. This test can be performed by making a hypothesis test or a simulation. When evaluating a hypothesis, it needs to be distinguished between results that can easily occur by chance and results that are highly improbable to occur by chance.

## Methods of Collecting Data

There are several different methods to collect data for statistical studies. Often, which method is best depends on the purpose of the study.

### Survey

A survey is when one or more characteristics of a population is studied by collecting data from every member of the sample. The data can be obtained by asking questions or making measurements.

### Experiment

An experiment involves a group of participants undergoing a specific treatment with the goal of collecting data about their reactions to the treatment. In some statistical studies it is necessary to conduct an experiment in order to collect the data. For example, this method is often used when studying the effects of a medical treatment.

### Observational Study

An observational study involves observing the chosen sample to gather data. The researcher does not interact with the sample or expose them to treatments, like in an experiment.

## Determine the type of each statistical study

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Determine the type of statistical study.

1. You want to determine what percent of customers in a local grocery store buys cheese. Data is collected by standing outside the store and asking the customers questions as they exit.
2. A team of researchers test a new vaccine against measles on 100 students who volunteered to participate.
3. A referendum in Belmar, New Jersey, on whether it should be compulsory for the shop owners in town to have a porcelain cat in the shop window.
4. Professor Potocoff conducts a study to determine if patients who are treated for high blood pressure have an increased risk of getting malaria. She does the study by analyzing information in a database at the hospital where she works.
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1. Here, one characteristic of a population is studied and every member of the sample is asked the same question. Therefore, it is a survey.
2. Here, the participants undergo a treatment — the vaccine. Thus, it is an experiment.
3. In a referendum, everyone in the population is asked the same question. Thus, it is a survey.
4. The professor gathers data from a database; she does not interact with the participants. As there is no treatment conducted, it is an observational study.